|
|
| (15 intermediate revisions by 7 users not shown) |
| Line 1: |
Line 1: |
| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-10-05 22:47:16 UTC</tt>.<br>
| | |
| : The original revision id was <tt>457120748</tt>.<br>
| | 578edo is [[enfactoring|enfactored]] in the [[5-limit]], [[tempering out]] [[32805/32768]] (schisma) with the same tuning as [[289edo]]. It tempers out 118098/117649 (stearnsma) which together with the schisma gives 7-limit [[pogo]] temperament, the 224 & 354 temperament. In the [[11-limit]] it tempers out [[540/539]] and [[4000/3993]] and provides the [[optimal patent val]] for 11-limit pogo and the planar temperament [[hades]], as well as other temperaments tempering out 540/539, the rank-4 temperament for which it also provides the optimal patent val. In the 13-limit, it tempers out [[729/728]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], and provides the optimal patent val for 13-limit pogo. |
| : The revision comment was: <tt></tt><br>
| | |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | === Prime harmonics === |
| <h4>Original Wikitext content:</h4>
| | {{Harmonics in equal|578|columns=11}} |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The //578 equal division// divides the octave into 578 equal parts of 2.076 cents each. It is contorted in the 5-limit, tempering out 32805/32768 with the same tuning as 289edo. It tempers out 10976/10935 and 65625/65536 in the 7-limit, supporting the 22&118 temperament, and 119098/117649 which together with the schisma gives 7-limit [[Schismatic family#Pogo|pogo temperament]], the 94&130 temperament. In the 11-limit it tempers out 540/539 and 4000/3993 and provides the [[optimal patent val]] for 11-limit pogo and the planar temperament [[Swetismic temperaments#Hades|hades]]. In the 13-limit, it tempers out 729/729, 1575/1573, 1716/1715 and 2080/2079, and provides the optimal patent val for 13-limit pogo, as well as other temperaments tempering out 1716/1715, the rank five temperament for which it also provides the optimal patent val. 578 factors as 2 * 17^2.</pre></div>
| | |
| <h4>Original HTML content:</h4>
| | === Subsets and supersets === |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>578edo</title></head><body>The <em>578 equal division</em> divides the octave into 578 equal parts of 2.076 cents each. It is contorted in the 5-limit, tempering out 32805/32768 with the same tuning as 289edo. It tempers out 10976/10935 and 65625/65536 in the 7-limit, supporting the 22&amp;118 temperament, and 119098/117649 which together with the schisma gives 7-limit <a class="wiki_link" href="/Schismatic%20family#Pogo">pogo temperament</a>, the 94&amp;130 temperament. In the 11-limit it tempers out 540/539 and 4000/3993 and provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for 11-limit pogo and the planar temperament <a class="wiki_link" href="/Swetismic%20temperaments#Hades">hades</a>. In the 13-limit, it tempers out 729/729, 1575/1573, 1716/1715 and 2080/2079, and provides the optimal patent val for 13-limit pogo, as well as other temperaments tempering out 1716/1715, the rank five temperament for which it also provides the optimal patent val. 578 factors as 2 * 17^2.</body></html></pre></div>
| | 578 factors as {{factorization|578}}, with divisors {{EDOs| 2, 17, 34, and 289 }}. |
| | |
| | [[Category:Swetismic]] |
| | [[Category:Hades]] |
| | [[Category:Pogo]] |